β-Galactosidase bound to DEAE-cellulose is used to hydrolyze lactose
to glucose and galactose in a plug flow bioreactor with a packed bed
of volume 100 liters and a voidage (ε) of 0.55. The K’m and
V’max for the immobilized enzyme are
0.72 g l−1 and
18 g l−1 h−1, respectively.
The lactose concentration in the feed stream is
20 g l−1, and a fractional conversion of 0.90 is desired.
Diffusional limitations may be ignored.
bioconversion will be
Feed Flow Rate Calculation for Lactose Hydrolysis in a Plug Flow Bioreactor
Immobilized enzyme reactors are widely used in biochemical engineering due to their stability and
reusability. In this problem, β-galactosidase immobilized on DEAE-cellulose is used to hydrolyze lactose
in a plug flow bioreactor (PFR). The objective is to calculate the feed flow rate required to achieve
a desired fractional conversion using Michaelis–Menten kinetics.
Given Data
- Packed bed volume = 100 L
- Voidage (ε) = 0.55
- Effective liquid volume = 55 L
- Feed lactose concentration (S0) = 20 g L-1
- Desired fractional conversion (X) = 0.90
- Km = 0.72 g L-1
- V′max = 18 g L-1 h-1
- Diffusional limitations are neglected
Design Equation for Plug Flow Bioreactor
For a plug flow bioreactor following Michaelis–Menten kinetics, the space time (τ) is given by:
τ = (1 / V′max) [ Km ln(1 / (1 − X)) + S0X ]
Step-by-Step Calculation
Substituting the given values:
τ = (1 / 18) [ 0.72 ln(1 / 0.1) + 20 × 0.9 ]
ln(10) = 2.3026
τ = (1 / 18) (1.66 + 18)
τ = 19.66 / 18 = 1.09 h
Feed Flow Rate Calculation
Space time is related to flow rate as:
τ = V / Q
Q = 55 / 1.09 ≈ 50.4 L h-1
Correct Answer
(A) 50 L h-1
Conclusion
Using the plug flow bioreactor design equation with Michaelis–Menten kinetics, the feed flow rate
required to achieve 90% lactose conversion is 50 L h-1.
